An important question from ML Agarwal of Class10 for board examination We have asked The sum of three numbers in AP is 30 and the ratio of first number to third number is 3:7. Find the numbers.

ML Agarwal(avichal publication) class 10, CBSE, Arithmetic Progression chapter 9 question no 24

Rajan@2021Guru

# The sum of three numbers in AP is 30 and the ratio of first number to third number is 3:7. Find the numbers.

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From the question, it is given that,

the sum of three numbers in A.P.Â =30

The ratio of the first number to the third number is 3: 7

Let us assume the 3 numbers which are in A.P. are,Â aâˆ’d,a,a+d

Now adding 3 numbersÂ =aâˆ’d+a+a+d=30

3a=30a=30/3a=10â€‹

Given ratioÂ 3:7=aâˆ’d:a+d

3/7=(aâˆ’d)/(a+d)

(aâˆ’d)7=3(a+d)

7aâˆ’7d=3a+3d7

aâˆ’3a=7d+3d

4a=10d

4(10)=10d

40=10d

d=40/10

d=4â€‹

Therefore, the numbers areÂ aâˆ’d=10âˆ’4=6

a=10

a+d=10+4=14

So,6,10,14,â€¦Â are in A.P.